The main goal of this work is the development of an efficient coupling algorithm for solving various fluid-structure-interaction (FSI) problems in three-dimensional domains for arbitrary elastic structures. Here, the fluid is assumed to be incompressible and Newtonian. The structure is made of an isotropic elastic material. Linear and geometrically non-linear models are used for structural problems with small and finite deformations, respectively. An explicit and an implicit loose coupling methods for the numerical simulation of FSI tasks have been developed. For this purpose the finite volume code FASTEST-3D has been applied to the fluid dynamic subproblem and the finite element program FEAP has been used for the structural dynamic subtask. For modelling the FSI, the pressure and shear forces of the fluid flow are projected into the structural nodes and applied as boundary conditions for the structure. To account for the fluid domain movement caused by the structural deformation, the fluid solver has been modified so that it can also treat problems described in Eulerian-Lagrangian (moving) coordinates. The fluid grid is updated to match the new domain boundaries using a linear interpolation. Hence, the space conservation law is added to the Navier-Stokes equations and a total mass conservation has been assured. In the explicit coupling method the information between the solvers is exchanged only once per time-step. On the other hand the implicit coupling strategy is based on a predictor-corrector scheme for finding the fluid-structure equilibrium at every time-step. The explicit coupling algorithm has been applied to problems with small deformations. However, this method is not suitable for dynamical problems with finite deformations because of its restriction on the time-step size. For these FSI problems the implicit coupling strategy is advantageous because it has no restriction on the time-step size. The predictor-corrector scheme has been successfully used to both steady and dynamic FSI tasks with finite deformations. The numerical investigation of the implicit coupling method showed that it has very good convergence properties. The proposed coupling strategies have successfully modelled the test examples. Therefore, they can be further applied to solve practical FSI problems. Moreover, depending on the generality of the used fluid and structural codes, the developed coupling methods are also able to simulate various FSI tasks.